A recently discovered novel alkylation catalyst mixture contains a hydrogen halide component in a sulfone diluent. While the components of the alkylation catalyst mixture are substantially immiscible with hydrocarbons, particularly, an alkylate product, the sulfone component is still slightly soluble in hydrocarbon. Consequently, there can be a small concentration of sulfone in an alkylate product produced by the catalytic alkylation of olefins by isoparaffins using as the catalyst a hydrogen halide in a sulfone diluent. The concentration of sulfone in the alkylate product can range upwardly to about 4000 parts per million by weight (ppmw). A high concentration of sulfone in the alkylate product is undesirable because of the use of alkylate as a motor gasoline blending material. The concentration of sulfone in the alkylate should be less than about 100 ppmw.